In [1]:
%matplotlib inline
%config InlineBackend.figure_format='retina'

from IPython.display import display, display_markdown

import warnings
warnings.simplefilter(action='ignore', category=FutureWarning)

import subprocess as sp
import numpy as np
import pandas as pd
import seaborn as sns
import arviz as az
import bambi
from copy import deepcopy

import matplotlib.pyplot as plt
plt.rcParams['figure.figsize'] = [10, 8]
plt.rcParams['figure.dpi'] = 150

from subs2vec.utensils import log_timer
from subs2vec.vecs import Vectors
from subs2vec.neighbors import compute_nn

import logging
logging.getLogger().setLevel(logging.WARNING)

def display_md(md, **kwargs):
    return display_markdown(md, raw=True, **kwargs)

def convert_notebook(title, output='html'):
    convert = sp.run(f'jupyter nbconvert {title}.ipynb --to {output} --output {title}.{output}'.split(' '))
    if convert.returncode == 0:
        display_md(f'Jupyter notebook `{title}` converted successfully.')
    else:
        display_md(f'Error: encountered problem converting Jupyter notebook `{title}`')

def norm(x):
    return x / np.linalg.norm(x, 2)

def standardize(x):
    return (x - x.mean()) / x.std()

sns.set(style='whitegrid')
pd.options.mode.chained_assignment = None

Loading and preparing data¶

In [2]:
df_joint = pd.read_csv('data/data_plus_predictors.tsv', sep='\t')
display(df_joint)
index group dimension pp_id color rating experiment self_vs_other art fiction ... sighted group_eff group_z original replication_1 replication_2 other self self_vs_other_eff self_vs_other_z
0 0 sighted cold-hot sighted_1 white 1 original self NaN NaN ... 1 1.0 0.211241 1 0 0 0 1 -1.0 -0.891882
1 1 sighted ripe-unripe sighted_1 white 7 original self NaN NaN ... 1 1.0 0.211241 1 0 0 0 1 -1.0 -0.891882
2 2 sighted new-old sighted_1 white 1 original self NaN NaN ... 1 1.0 0.211241 1 0 0 0 1 -1.0 -0.891882
3 3 sighted submissive-aggressive sighted_1 white 1 original self NaN NaN ... 1 1.0 0.211241 1 0 0 0 1 -1.0 -0.891882
4 4 sighted selfless-jealous sighted_1 white 1 original self NaN NaN ... 1 1.0 0.211241 1 0 0 0 1 -1.0 -0.891882
... ... ... ... ... ... ... ... ... ... ... ... ... ... ... ... ... ... ... ... ... ...
42975 28507 sighted light-heavy sighted_68129 red 5 replication_2 other 11.0 0.0 ... 1 1.0 0.211241 0 0 1 1 0 1.0 1.121199
42976 28508 sighted relaxed-tense sighted_68129 red 5 replication_2 other 11.0 0.0 ... 1 1.0 0.211241 0 0 1 1 0 1.0 1.121199
42977 28509 sighted alive-dead sighted_68129 red 6 replication_2 other 11.0 0.0 ... 1 1.0 0.211241 0 0 1 1 0 1.0 1.121199
42978 28510 sighted fast-slow sighted_68129 red 3 replication_2 other 11.0 0.0 ... 1 1.0 0.211241 0 0 1 1 0 1.0 1.121199
42979 28511 sighted high-low sighted_68129 red 2 replication_2 other 11.0 0.0 ... 1 1.0 0.211241 0 0 1 1 0 1.0 1.121199

42980 rows × 76 columns

In [3]:
corr = df_joint[[
    'cosine_fic_z',
    'cosine_fic_no_1st_order_z',
    'cosine_fic_no_neighbors_weak_z',
    'cosine_fic_no_neighbors_strong_z',
    'cosine_fic_no_mediators_z',
]].corr()
display(corr.round(2))
cosine_fic_z cosine_fic_no_1st_order_z cosine_fic_no_neighbors_weak_z cosine_fic_no_neighbors_strong_z cosine_fic_no_mediators_z
cosine_fic_z 1.00 0.92 0.86 0.75 0.41
cosine_fic_no_1st_order_z 0.92 1.00 0.86 0.79 0.43
cosine_fic_no_neighbors_weak_z 0.86 0.86 1.00 0.75 0.48
cosine_fic_no_neighbors_strong_z 0.75 0.79 0.75 1.00 0.44
cosine_fic_no_mediators_z 0.41 0.43 0.48 0.44 1.00

Differences between modified versions of the COCA-fiction corpus¶

COCA-fiction¶

In [4]:
m_fic = bambi.Model('rating_z ~ 1'
    + ' + group_eff*frequency_z'
    + ' + group_eff*concreteness_z'
    + ' + group_eff*cosine_fic_z'
    + ' + group_eff*swow_all_z'
    + ' + (1 + frequency_z + concreteness_z + cosine_fic_z + swow_all_z|pp_id)'
    + ' + (1 + group_eff|dimension)'
    + ' + (1 + group_eff|color)',
    df_joint[df_joint['self_vs_other'] == 'self']
)
r_fic = m_fic.fit(
    init='advi+adapt_diag',
    chains=4,
    draws=1000,
    tune=1000,
    n_init=10000,
    target_accept=.95,
)

Auto-assigning NUTS sampler...
[INFO] Auto-assigning NUTS sampler...
Initializing NUTS using advi+adapt_diag...
[INFO] Initializing NUTS using advi+adapt_diag...
100.00% [10000/10000 00:33<00:00 Average Loss = 42,785] 
Finished [100%]: Average Loss = 42,754
[INFO] Finished [100%]: Average Loss = 42,754
Multiprocess sampling (4 chains in 4 jobs)
[INFO] Multiprocess sampling (4 chains in 4 jobs)
NUTS: [Intercept, group_eff, frequency_z, group_eff:frequency_z, concreteness_z, group_eff:concreteness_z, cosine_fic_z, group_eff:cosine_fic_z, swow_all_z, group_eff:swow_all_z, 1|pp_id_sigma, 1|pp_id_offset, frequency_z|pp_id_sigma, frequency_z|pp_id_offset, concreteness_z|pp_id_sigma, concreteness_z|pp_id_offset, cosine_fic_z|pp_id_sigma, cosine_fic_z|pp_id_offset, swow_all_z|pp_id_sigma, swow_all_z|pp_id_offset, 1|dimension_sigma, 1|dimension_offset, group_eff|dimension_sigma, group_eff|dimension_offset, 1|color_sigma, 1|color_offset, group_eff|color_sigma, group_eff|color_offset, rating_z_sigma]
[INFO] NUTS: [Intercept, group_eff, frequency_z, group_eff:frequency_z, concreteness_z, group_eff:concreteness_z, cosine_fic_z, group_eff:cosine_fic_z, swow_all_z, group_eff:swow_all_z, 1|pp_id_sigma, 1|pp_id_offset, frequency_z|pp_id_sigma, frequency_z|pp_id_offset, concreteness_z|pp_id_sigma, concreteness_z|pp_id_offset, cosine_fic_z|pp_id_sigma, cosine_fic_z|pp_id_offset, swow_all_z|pp_id_sigma, swow_all_z|pp_id_offset, 1|dimension_sigma, 1|dimension_offset, group_eff|dimension_sigma, group_eff|dimension_offset, 1|color_sigma, 1|color_offset, group_eff|color_sigma, group_eff|color_offset, rating_z_sigma]
100.00% [8000/8000 32:46<00:00 Sampling 4 chains, 0 divergences] 
Sampling 4 chains for 1_000 tune and 1_000 draw iterations (4_000 + 4_000 draws total) took 1976 seconds.
[INFO] Sampling 4 chains for 1_000 tune and 1_000 draw iterations (4_000 + 4_000 draws total) took 1976 seconds.
In [5]:
# compute and plot conditional effect of cosine in sighted and blind groups
trace = deepcopy(r_fic.posterior)
# effect of cosine in blind group in orginal experiment
trace['blind:cosine_fic_z'] = trace['cosine_fic_z'] - trace['group_eff:cosine_fic_z']
    # effect of cosine in sighted group across both experiments
trace['sighted:cosine_fic_z'] = trace['cosine_fic_z'] + trace['group_eff:cosine_fic_z']

varnames = ['blind:cosine_fic_z', 'sighted:cosine_fic_z']
g = az.plot_forest(trace, combined=True, hdi_prob=.95,
                   figsize=[9, .6 + len(varnames) * .3],
                   var_names=varnames)
g[0].axvline(0, color='.8', linewidth=2);

COCA-fiction without 1st order cooccurrence of color and dimension words¶

In [6]:
m_fic_filtered = bambi.Model('rating_z ~ 1'
    + ' + group_eff*frequency_z'
    + ' + group_eff*concreteness_z'
    + ' + group_eff*cosine_fic_no_1st_order_z'
    + ' + group_eff*swow_all_z'
    + ' + (1 + frequency_z + concreteness_z + cosine_fic_no_1st_order_z + swow_all_z|pp_id)'
    + ' + (1 + group_eff|dimension)'
    + ' + (1 + group_eff|color)',
    df_joint[df_joint['self_vs_other'] == 'self']
)
r_fic_filtered = m_fic_filtered.fit(
    init='advi+adapt_diag',
    chains=4,
    draws=1000,
    tune=1000,
    n_init=10000,
    target_accept=.95,
)

Auto-assigning NUTS sampler...
[INFO] Auto-assigning NUTS sampler...
Initializing NUTS using advi+adapt_diag...
[INFO] Initializing NUTS using advi+adapt_diag...
100.00% [10000/10000 00:21<00:00 Average Loss = 42,666] 
Finished [100%]: Average Loss = 42,645
[INFO] Finished [100%]: Average Loss = 42,645
Multiprocess sampling (4 chains in 4 jobs)
[INFO] Multiprocess sampling (4 chains in 4 jobs)
NUTS: [Intercept, group_eff, frequency_z, group_eff:frequency_z, concreteness_z, group_eff:concreteness_z, cosine_fic_no_1st_order_z, group_eff:cosine_fic_no_1st_order_z, swow_all_z, group_eff:swow_all_z, 1|pp_id_sigma, 1|pp_id_offset, frequency_z|pp_id_sigma, frequency_z|pp_id_offset, concreteness_z|pp_id_sigma, concreteness_z|pp_id_offset, cosine_fic_no_1st_order_z|pp_id_sigma, cosine_fic_no_1st_order_z|pp_id_offset, swow_all_z|pp_id_sigma, swow_all_z|pp_id_offset, 1|dimension_sigma, 1|dimension_offset, group_eff|dimension_sigma, group_eff|dimension_offset, 1|color_sigma, 1|color_offset, group_eff|color_sigma, group_eff|color_offset, rating_z_sigma]
[INFO] NUTS: [Intercept, group_eff, frequency_z, group_eff:frequency_z, concreteness_z, group_eff:concreteness_z, cosine_fic_no_1st_order_z, group_eff:cosine_fic_no_1st_order_z, swow_all_z, group_eff:swow_all_z, 1|pp_id_sigma, 1|pp_id_offset, frequency_z|pp_id_sigma, frequency_z|pp_id_offset, concreteness_z|pp_id_sigma, concreteness_z|pp_id_offset, cosine_fic_no_1st_order_z|pp_id_sigma, cosine_fic_no_1st_order_z|pp_id_offset, swow_all_z|pp_id_sigma, swow_all_z|pp_id_offset, 1|dimension_sigma, 1|dimension_offset, group_eff|dimension_sigma, group_eff|dimension_offset, 1|color_sigma, 1|color_offset, group_eff|color_sigma, group_eff|color_offset, rating_z_sigma]
100.00% [8000/8000 22:42<00:00 Sampling 4 chains, 0 divergences] 
Sampling 4 chains for 1_000 tune and 1_000 draw iterations (4_000 + 4_000 draws total) took 1369 seconds.
[INFO] Sampling 4 chains for 1_000 tune and 1_000 draw iterations (4_000 + 4_000 draws total) took 1369 seconds.
In [7]:
# compute and plot conditional effect of cosine in sighted and blind groups
trace_filtered = deepcopy(r_fic_filtered.posterior)
# effect of cosine in blind group in orginal experiment
trace['blind:cosine_fic_no_1st_order_z'] = (trace_filtered['cosine_fic_no_1st_order_z']
                                            - trace_filtered['group_eff:cosine_fic_no_1st_order_z'])
# effect of cosine in sighted group across both experiments
trace['sighted:cosine_fic_no_1st_order_z'] = (trace_filtered['cosine_fic_no_1st_order_z']
                                              + trace_filtered['group_eff:cosine_fic_no_1st_order_z'])

varnames = [
    'blind:cosine_fic_z', 'sighted:cosine_fic_z',
    'blind:cosine_fic_no_1st_order_z', 'sighted:cosine_fic_no_1st_order_z',
]
g = az.plot_forest(trace, combined=True, hdi_prob=.95,
                   figsize=[9, .6 + len(varnames) * .3],
                   var_names=varnames)
g[0].axvline(0, color='.8', linewidth=2);

COCA-fiction without 25 nearest neighbors of each dimension word, weak and strong methods¶

In [8]:
m_fic_noneighbors_weak = bambi.Model('rating_z ~ 1'
    + ' + group_eff*frequency_z'
    + ' + group_eff*concreteness_z'
    + ' + group_eff*cosine_fic_no_neighbors_weak_z'
    + ' + group_eff*swow_all_z'
    + ' + (1 + frequency_z + concreteness_z + cosine_fic_no_neighbors_weak_z + swow_all_z|pp_id)'
    + ' + (1 + group_eff|dimension)'
    + ' + (1 + group_eff|color)',
    df_joint[df_joint['self_vs_other'] == 'self']
)
r_fic_noneighbors_weak = m_fic_noneighbors_weak.fit(
    init='advi+adapt_diag',
    chains=4,
    draws=1000,
    tune=1000,
    n_init=10000,
    target_accept=.95,
)

Auto-assigning NUTS sampler...
[INFO] Auto-assigning NUTS sampler...
Initializing NUTS using advi+adapt_diag...
[INFO] Initializing NUTS using advi+adapt_diag...
100.00% [10000/10000 00:24<00:00 Average Loss = 42,792] 
Finished [100%]: Average Loss = 42,774
[INFO] Finished [100%]: Average Loss = 42,774
Multiprocess sampling (4 chains in 4 jobs)
[INFO] Multiprocess sampling (4 chains in 4 jobs)
NUTS: [Intercept, group_eff, frequency_z, group_eff:frequency_z, concreteness_z, group_eff:concreteness_z, cosine_fic_no_neighbors_weak_z, group_eff:cosine_fic_no_neighbors_weak_z, swow_all_z, group_eff:swow_all_z, 1|pp_id_sigma, 1|pp_id_offset, frequency_z|pp_id_sigma, frequency_z|pp_id_offset, concreteness_z|pp_id_sigma, concreteness_z|pp_id_offset, cosine_fic_no_neighbors_weak_z|pp_id_sigma, cosine_fic_no_neighbors_weak_z|pp_id_offset, swow_all_z|pp_id_sigma, swow_all_z|pp_id_offset, 1|dimension_sigma, 1|dimension_offset, group_eff|dimension_sigma, group_eff|dimension_offset, 1|color_sigma, 1|color_offset, group_eff|color_sigma, group_eff|color_offset, rating_z_sigma]
[INFO] NUTS: [Intercept, group_eff, frequency_z, group_eff:frequency_z, concreteness_z, group_eff:concreteness_z, cosine_fic_no_neighbors_weak_z, group_eff:cosine_fic_no_neighbors_weak_z, swow_all_z, group_eff:swow_all_z, 1|pp_id_sigma, 1|pp_id_offset, frequency_z|pp_id_sigma, frequency_z|pp_id_offset, concreteness_z|pp_id_sigma, concreteness_z|pp_id_offset, cosine_fic_no_neighbors_weak_z|pp_id_sigma, cosine_fic_no_neighbors_weak_z|pp_id_offset, swow_all_z|pp_id_sigma, swow_all_z|pp_id_offset, 1|dimension_sigma, 1|dimension_offset, group_eff|dimension_sigma, group_eff|dimension_offset, 1|color_sigma, 1|color_offset, group_eff|color_sigma, group_eff|color_offset, rating_z_sigma]
100.00% [8000/8000 22:49<00:00 Sampling 4 chains, 0 divergences] 
Sampling 4 chains for 1_000 tune and 1_000 draw iterations (4_000 + 4_000 draws total) took 1378 seconds.
[INFO] Sampling 4 chains for 1_000 tune and 1_000 draw iterations (4_000 + 4_000 draws total) took 1378 seconds.
In [9]:
# compute and plot conditional effect of cosine in sighted and blind groups
trace_weak = deepcopy(r_fic_noneighbors_weak.posterior)
# effect of cosine in blind group in orginal experiment
trace['blind:cosine_fic_no_neighbors_weak_z'] = (trace_weak['cosine_fic_no_neighbors_weak_z']
                                                 - trace_weak['group_eff:cosine_fic_no_neighbors_weak_z'])
# effect of cosine in sighted group across both experiments
trace['sighted:cosine_fic_no_neighbors_weak_z'] = (trace_weak['cosine_fic_no_neighbors_weak_z']
                                                   + trace_weak['group_eff:cosine_fic_no_neighbors_weak_z'])

varnames = [
    'blind:cosine_fic_z', 'sighted:cosine_fic_z',
    'blind:cosine_fic_no_1st_order_z', 'sighted:cosine_fic_no_1st_order_z',
    'blind:cosine_fic_no_neighbors_weak_z', 'sighted:cosine_fic_no_neighbors_weak_z',
]
g = az.plot_forest(trace, combined=True, hdi_prob=.95,
                   figsize=[9, .6 + len(varnames) * .3],
                   var_names=varnames)
g[0].axvline(0, color='.8', linewidth=2);
In [10]:
m_fic_noneighbors_strong = bambi.Model('rating_z ~ 1'
    + ' + group_eff*frequency_z'
    + ' + group_eff*concreteness_z'
    + ' + group_eff*cosine_fic_no_neighbors_strong_z'
    + ' + group_eff*swow_all_z'
    + ' + (1 + frequency_z + concreteness_z + cosine_fic_no_neighbors_strong_z + swow_all_z|pp_id)'
    + ' + (1 + group_eff|dimension)'
    + ' + (1 + group_eff|color)',
    df_joint[df_joint['self_vs_other'] == 'self']
)
r_fic_noneighbors_strong = m_fic_noneighbors_strong.fit(
    init='advi+adapt_diag',
    chains=4,
    draws=1000,
    tune=1000,
    n_init=10000,
    target_accept=.95,
)

Auto-assigning NUTS sampler...
[INFO] Auto-assigning NUTS sampler...
Initializing NUTS using advi+adapt_diag...
[INFO] Initializing NUTS using advi+adapt_diag...
100.00% [10000/10000 00:22<00:00 Average Loss = 42,841] 
Finished [100%]: Average Loss = 42,825
[INFO] Finished [100%]: Average Loss = 42,825
Multiprocess sampling (4 chains in 4 jobs)
[INFO] Multiprocess sampling (4 chains in 4 jobs)
NUTS: [Intercept, group_eff, frequency_z, group_eff:frequency_z, concreteness_z, group_eff:concreteness_z, cosine_fic_no_neighbors_strong_z, group_eff:cosine_fic_no_neighbors_strong_z, swow_all_z, group_eff:swow_all_z, 1|pp_id_sigma, 1|pp_id_offset, frequency_z|pp_id_sigma, frequency_z|pp_id_offset, concreteness_z|pp_id_sigma, concreteness_z|pp_id_offset, cosine_fic_no_neighbors_strong_z|pp_id_sigma, cosine_fic_no_neighbors_strong_z|pp_id_offset, swow_all_z|pp_id_sigma, swow_all_z|pp_id_offset, 1|dimension_sigma, 1|dimension_offset, group_eff|dimension_sigma, group_eff|dimension_offset, 1|color_sigma, 1|color_offset, group_eff|color_sigma, group_eff|color_offset, rating_z_sigma]
[INFO] NUTS: [Intercept, group_eff, frequency_z, group_eff:frequency_z, concreteness_z, group_eff:concreteness_z, cosine_fic_no_neighbors_strong_z, group_eff:cosine_fic_no_neighbors_strong_z, swow_all_z, group_eff:swow_all_z, 1|pp_id_sigma, 1|pp_id_offset, frequency_z|pp_id_sigma, frequency_z|pp_id_offset, concreteness_z|pp_id_sigma, concreteness_z|pp_id_offset, cosine_fic_no_neighbors_strong_z|pp_id_sigma, cosine_fic_no_neighbors_strong_z|pp_id_offset, swow_all_z|pp_id_sigma, swow_all_z|pp_id_offset, 1|dimension_sigma, 1|dimension_offset, group_eff|dimension_sigma, group_eff|dimension_offset, 1|color_sigma, 1|color_offset, group_eff|color_sigma, group_eff|color_offset, rating_z_sigma]
100.00% [8000/8000 22:34<00:00 Sampling 4 chains, 0 divergences] 
Sampling 4 chains for 1_000 tune and 1_000 draw iterations (4_000 + 4_000 draws total) took 1362 seconds.
[INFO] Sampling 4 chains for 1_000 tune and 1_000 draw iterations (4_000 + 4_000 draws total) took 1362 seconds.
In [11]:
# compute and plot conditional effect of cosine in sighted and blind groups
trace_strong = deepcopy(r_fic_noneighbors_strong.posterior)
# effect of cosine in blind group in orginal experiment
trace['blind:cosine_fic_no_neighbors_strong_z'] = (trace_strong['cosine_fic_no_neighbors_strong_z']
                                                   - trace_strong['group_eff:cosine_fic_no_neighbors_strong_z'])
# effect of cosine in sighted group across both experiments
trace['sighted:cosine_fic_no_neighbors_strong_z'] = (trace_strong['cosine_fic_no_neighbors_strong_z']
                                                     + trace_strong['group_eff:cosine_fic_no_neighbors_strong_z'])

varnames = [
    'blind:cosine_fic_z', 'sighted:cosine_fic_z',
    'blind:cosine_fic_no_1st_order_z', 'sighted:cosine_fic_no_1st_order_z',
    'blind:cosine_fic_no_neighbors_weak_z', 'sighted:cosine_fic_no_neighbors_weak_z',
    'blind:cosine_fic_no_neighbors_strong_z', 'sighted:cosine_fic_no_neighbors_strong_z',
]
g = az.plot_forest(trace, combined=True, hdi_prob=.95,
                   figsize=[9, .6 + len(varnames) * .3],
                   var_names=varnames)
g[0].axvline(0, color='.8', linewidth=2);

COCA-fiction without names provided by participants for color-semantic dimensions¶

In [12]:
m_fic_nonames = bambi.Model('rating_z ~ 1'
    + ' + group_eff*frequency_z'
    + ' + group_eff*concreteness_z'
    + ' + group_eff*cosine_fic_no_mediators_z'
    + ' + group_eff*swow_all_z'
    + ' + (1 + frequency_z + concreteness_z + cosine_fic_no_mediators_z + swow_all_z|pp_id)'
    + ' + (1 + group_eff|dimension)'
    + ' + (1 + group_eff|color)',
    df_joint[df_joint['self_vs_other'] == 'self']
)
r_fic_nonames = m_fic_nonames.fit(
    init='advi+adapt_diag',
    chains=4,
    draws=1000,
    tune=1000,
    n_init=10000,
    target_accept=.95,
)

Auto-assigning NUTS sampler...
[INFO] Auto-assigning NUTS sampler...
Initializing NUTS using advi+adapt_diag...
[INFO] Initializing NUTS using advi+adapt_diag...
100.00% [10000/10000 00:23<00:00 Average Loss = 42,654] 
Finished [100%]: Average Loss = 42,638
[INFO] Finished [100%]: Average Loss = 42,638
Multiprocess sampling (4 chains in 4 jobs)
[INFO] Multiprocess sampling (4 chains in 4 jobs)
NUTS: [Intercept, group_eff, frequency_z, group_eff:frequency_z, concreteness_z, group_eff:concreteness_z, cosine_fic_no_mediators_z, group_eff:cosine_fic_no_mediators_z, swow_all_z, group_eff:swow_all_z, 1|pp_id_sigma, 1|pp_id_offset, frequency_z|pp_id_sigma, frequency_z|pp_id_offset, concreteness_z|pp_id_sigma, concreteness_z|pp_id_offset, cosine_fic_no_mediators_z|pp_id_sigma, cosine_fic_no_mediators_z|pp_id_offset, swow_all_z|pp_id_sigma, swow_all_z|pp_id_offset, 1|dimension_sigma, 1|dimension_offset, group_eff|dimension_sigma, group_eff|dimension_offset, 1|color_sigma, 1|color_offset, group_eff|color_sigma, group_eff|color_offset, rating_z_sigma]
[INFO] NUTS: [Intercept, group_eff, frequency_z, group_eff:frequency_z, concreteness_z, group_eff:concreteness_z, cosine_fic_no_mediators_z, group_eff:cosine_fic_no_mediators_z, swow_all_z, group_eff:swow_all_z, 1|pp_id_sigma, 1|pp_id_offset, frequency_z|pp_id_sigma, frequency_z|pp_id_offset, concreteness_z|pp_id_sigma, concreteness_z|pp_id_offset, cosine_fic_no_mediators_z|pp_id_sigma, cosine_fic_no_mediators_z|pp_id_offset, swow_all_z|pp_id_sigma, swow_all_z|pp_id_offset, 1|dimension_sigma, 1|dimension_offset, group_eff|dimension_sigma, group_eff|dimension_offset, 1|color_sigma, 1|color_offset, group_eff|color_sigma, group_eff|color_offset, rating_z_sigma]
100.00% [8000/8000 16:32<00:00 Sampling 4 chains, 0 divergences] 
Sampling 4 chains for 1_000 tune and 1_000 draw iterations (4_000 + 4_000 draws total) took 1001 seconds.
[INFO] Sampling 4 chains for 1_000 tune and 1_000 draw iterations (4_000 + 4_000 draws total) took 1001 seconds.
In [13]:
# compute and plot conditional effect of cosine in sighted and blind groups
trace_none = deepcopy(r_fic_nonames.posterior)
# effect of cosine in blind group in orginal experiment
trace['blind:cosine_fic_no_mediators_z'] = (trace_none['cosine_fic_no_mediators_z']
                                            - trace_none['group_eff:cosine_fic_no_mediators_z'])
# effect of cosine in sighted group across both experiments
trace['sighted:cosine_fic_no_mediators_z'] = (trace_none['cosine_fic_no_mediators_z']
                                              + trace_none['group_eff:cosine_fic_no_mediators_z'])

varnames = [
    'blind:cosine_fic_z', 'sighted:cosine_fic_z',
    'blind:cosine_fic_no_1st_order_z', 'sighted:cosine_fic_no_1st_order_z',
    'blind:cosine_fic_no_neighbors_weak_z', 'sighted:cosine_fic_no_neighbors_weak_z',
    'blind:cosine_fic_no_neighbors_strong_z', 'sighted:cosine_fic_no_neighbors_strong_z',
    'blind:cosine_fic_no_mediators_z', 'sighted:cosine_fic_no_mediators_z',
]
g = az.plot_forest(trace, combined=True, hdi_prob=.95,
                   figsize=[9, .6 + len(varnames) * .3],
                   var_names=varnames)
g[0].axvline(0, color='.8', linewidth=2);
In [16]:
varnames = [
    'sighted:cosine_fic_z',
    'sighted:cosine_fic_no_1st_order_z',
    'sighted:cosine_fic_no_neighbors_weak_z',
    'sighted:cosine_fic_no_neighbors_strong_z',
    'sighted:cosine_fic_no_mediators_z',
    'blind:cosine_fic_z',
    'blind:cosine_fic_no_1st_order_z',
    'blind:cosine_fic_no_neighbors_weak_z',
    'blind:cosine_fic_no_neighbors_strong_z',
    'blind:cosine_fic_no_mediators_z',
]
trace_df = az.summary(trace, hdi_prob=.95, var_names=varnames).reset_index()
sns.set(palette='colorblind', style='whitegrid')
trace_df['group'] = trace_df['index'].apply(lambda x: x.split(':')[0])
trace_df['predictor'] = trace_df['index'].apply(lambda x: x.split(':')[1])
g, ax = plt.subplots(figsize=[3.2, 3.2])
ax.axvline(0, color='.8', linewidth=2)
order = [
    'cosine_fic_z',
    'cosine_fic_no_1st_order_z',
    'cosine_fic_no_neighbors_weak_z',
    'cosine_fic_no_neighbors_strong_z',
    'cosine_fic_no_mediators_z',
]
sns.pointplot(data=trace_df, hue='group', x='mean', y='predictor', markers=['^', 'o'],
              join=False, ax=ax, order=order,
              palette=sns.color_palette()[0:], dodge=.2)
hdi_df = trace_df.melt(id_vars=['predictor', 'group'], value_vars=['hdi_2.5%', 'hdi_97.5%'])
sns.pointplot(data=hdi_df, hue='group', markers='', x='value', order=order,
              y='predictor', ax=ax, join=False,
              palette=sns.color_palette()[0:], dodge=.2)
ax.set(xlim=[-.1, .5], xticks=[-.1, 0, .1, .2, .3, .4, .5],
       ylabel='', xlabel='effect size (standardized coefficient)',
       #title='95% CIs for embedding projections\nafter altering corpora',
       title=''
)
ax.set(yticklabels=[
    'COCA-fiction projection',
    'COCA-fiction without\n1st order co-occ. (-1%)',
    'COCA-fiction without\n neighbors [weak] (-3%)',
    'COCA-fiction without\n neighbors [strong] (-57%)',
    'COCA-fiction without\ncommon mediators (-35%)',
])
labels = ax.get_legend_handles_labels()
ax.legend(handles=labels[0][:2], labels=labels[1][:2],
          bbox_to_anchor=(1, 1), loc=2, borderaxespad=0, frameon=False)
plt.savefig('figures/corpus_modification_forest.pdf', bbox_inches='tight')

/Users/jvparidon/.pyenv/versions/3.10.8/lib/python3.10/site-packages/seaborn/categorical.py:1728: UserWarning: You passed a edgecolor/edgecolors ((0.00392156862745098, 0.45098039215686275, 0.6980392156862745)) for an unfilled marker ('').  Matplotlib is ignoring the edgecolor in favor of the facecolor.  This behavior may change in the future.
  ax.scatter(x, y, label=hue_level,
/Users/jvparidon/.pyenv/versions/3.10.8/lib/python3.10/site-packages/seaborn/categorical.py:1728: UserWarning: You passed a edgecolor/edgecolors ((0.8705882352941177, 0.5607843137254902, 0.0196078431372549)) for an unfilled marker ('').  Matplotlib is ignoring the edgecolor in favor of the facecolor.  This behavior may change in the future.
  ax.scatter(x, y, label=hue_level,
In [15]:
display(az.summary(trace, hdi_prob=.95, var_names=varnames))
mean sd hdi_2.5% hdi_97.5% mcse_mean mcse_sd ess_bulk ess_tail r_hat
sighted:cosine_fic_z 0.431 0.015 0.403 0.460 0.000 0.000 4537.0 3411.0 1.0
sighted:cosine_fic_no_1st_order_z 0.394 0.014 0.366 0.420 0.000 0.000 4346.0 3481.0 1.0
sighted:cosine_fic_no_neighbors_weak_z 0.330 0.013 0.306 0.356 0.000 0.000 4509.0 2535.0 1.0
sighted:cosine_fic_no_neighbors_strong_z 0.312 0.014 0.286 0.341 0.000 0.000 4956.0 3255.0 1.0
sighted:cosine_fic_no_mediators_z 0.092 0.010 0.073 0.111 0.000 0.000 6533.0 3456.0 1.0
blind:cosine_fic_z 0.359 0.045 0.265 0.443 0.001 0.001 1763.0 2230.0 1.0
blind:cosine_fic_no_1st_order_z 0.251 0.043 0.164 0.331 0.001 0.001 2059.0 2070.0 1.0
blind:cosine_fic_no_neighbors_weak_z 0.216 0.040 0.138 0.294 0.001 0.001 2136.0 2257.0 1.0
blind:cosine_fic_no_neighbors_strong_z 0.157 0.046 0.071 0.248 0.001 0.001 1655.0 2214.0 1.0
blind:cosine_fic_no_mediators_z 0.079 0.029 0.027 0.140 0.001 0.000 1930.0 2490.0 1.0

Comparing models on leave-one-out validation score¶

Instead of using conditional effect sizes from the models as a comparison, we can also compare the models on their out-of-sample predictive accuracy. Essentially we're looking to see which predictor, if included, makes the model worst.
Using prediction/cross-validation for model comparison has distinct advantages in some situations, but in our case (when we're not varying model complexity or structure, but only replacing a single predictor) the results will probably match our inferences from the conditional effect size plots.

In [16]:
display(az.compare({
    'intact COCA fiction': r_fic,
    '1st order removed': r_fic_filtered,
    'semantic neighbors removed (weak)': r_fic_noneighbors_weak,
    'semantic neighbors removed (strong)': r_fic_noneighbors_strong,
    'salient labels removed': r_fic_nonames,
}).round(2))

/Users/jvparidon/.pyenv/versions/3.10.8/lib/python3.10/site-packages/arviz/stats/stats.py:802: UserWarning: Estimated shape parameter of Pareto distribution is greater than 0.7 for one or more samples. You should consider using a more robust model, this is because importance sampling is less likely to work well if the marginal posterior and LOO posterior are very different. This is more likely to happen with a non-robust model and highly influential observations.
  warnings.warn(
/Users/jvparidon/.pyenv/versions/3.10.8/lib/python3.10/site-packages/arviz/stats/stats.py:802: UserWarning: Estimated shape parameter of Pareto distribution is greater than 0.7 for one or more samples. You should consider using a more robust model, this is because importance sampling is less likely to work well if the marginal posterior and LOO posterior are very different. This is more likely to happen with a non-robust model and highly influential observations.
  warnings.warn(
/Users/jvparidon/.pyenv/versions/3.10.8/lib/python3.10/site-packages/arviz/stats/stats.py:802: UserWarning: Estimated shape parameter of Pareto distribution is greater than 0.7 for one or more samples. You should consider using a more robust model, this is because importance sampling is less likely to work well if the marginal posterior and LOO posterior are very different. This is more likely to happen with a non-robust model and highly influential observations.
  warnings.warn(
/Users/jvparidon/.pyenv/versions/3.10.8/lib/python3.10/site-packages/arviz/stats/stats.py:802: UserWarning: Estimated shape parameter of Pareto distribution is greater than 0.7 for one or more samples. You should consider using a more robust model, this is because importance sampling is less likely to work well if the marginal posterior and LOO posterior are very different. This is more likely to happen with a non-robust model and highly influential observations.
  warnings.warn(
/Users/jvparidon/.pyenv/versions/3.10.8/lib/python3.10/site-packages/arviz/stats/stats.py:802: UserWarning: Estimated shape parameter of Pareto distribution is greater than 0.7 for one or more samples. You should consider using a more robust model, this is because importance sampling is less likely to work well if the marginal posterior and LOO posterior are very different. This is more likely to happen with a non-robust model and highly influential observations.
  warnings.warn(
rank elpd_loo p_loo elpd_diff weight se dse warning scale
1st order removed 0 -32694.74 403.23 0.00 0.56 105.14 0.00 True log
intact COCA fiction 1 -32722.68 394.34 27.94 0.44 105.08 22.39 True log
semantic neighbors removed (weak) 2 -32887.34 351.21 192.60 0.00 104.24 23.53 True log
semantic neighbors removed (strong) 3 -32981.03 353.12 286.29 0.01 104.13 28.65 True log
salient labels removed 4 -33217.15 341.15 522.41 0.00 103.50 31.80 True log

As expected, the no-mediator-words model fared worst, whereas filtering only first-order co-occurrences made exactly no difference with the unfiltered corpus whatsoever. (In fact, the first-order filtered model looks slightly better here, but judging by the assigned model weights it's pretty much a toss-up.)
Removing semantic neighbors and removing salient names/labels seems to be fairly equivalent here, as well. Since removing salient labels was a much more targeted intervention (much smaller percentage of the corpus removed), that seems to have been the intervention that was most effective at identifying meaningful training samples.

The comparison algorithm does warn that the shape parameter of the pareto distribution is too large for some observations. This is common with hierarchical models and shouldn't be a problem if it concerns only a few observations. We can check this by inspecting the LOO-statistics more closely.

In [17]:
az.loo(r_fic_nonames)

/Users/jvparidon/.pyenv/versions/3.9.4/lib/python3.9/site-packages/arviz/stats/stats.py:802: UserWarning: Estimated shape parameter of Pareto distribution is greater than 0.7 for one or more samples. You should consider using a more robust model, this is because importance sampling is less likely to work well if the marginal posterior and LOO posterior are very different. This is more likely to happen with a non-robust model and highly influential observations.
  warnings.warn(
Out[17]:
Computed from 4000 posterior samples and 23938 observations log-likelihood matrix.

         Estimate       SE
elpd_loo -33219.13   103.52
p_loo      342.62        -

There has been a warning during the calculation. Please check the results.
------

Pareto k diagnostic values:
                         Count   Pct.
(-Inf, 0.5]   (good)     23891   99.8%
 (0.5, 0.7]   (ok)          39    0.2%
   (0.7, 1]   (bad)          8    0.0%
   (1, Inf)   (very bad)     0    0.0%

It appears that for the no labels model, for instance, there are only a few observations in the "bad" range. This is not overly problematic given the nearly 24,000 observations that are in the correct range.

Visual model diagnostics¶

R-hat and other Markov chain diagnostics looked good, but it's still worth doing a few quick visual model checks.

Quick look at the trace plots¶

We want all the Markov chains for a single variable to look lined up in the density plot on the left, but nice and fuzzy (i.e. not autocorrelated) on the right.

In [18]:
g = az.plot_trace(r_fic, var_names=['Intercept', 'group_eff', 'cosine_fic_z', 'group_eff:cosine_fic_z'])
plt.tight_layout()
In [19]:
g = az.plot_trace(r_fic_filtered, var_names=['Intercept',
                                             'group_eff',
                                             'cosine_fic_no_1st_order_z',
                                             'group_eff:cosine_fic_no_1st_order_z'])
plt.tight_layout()
In [20]:
g = az.plot_trace(r_fic_noneighbors_weak, var_names=['Intercept',
                                                     'group_eff',
                                                     'cosine_fic_no_neighbors_weak_z',
                                                     'group_eff:cosine_fic_no_neighbors_weak_z'])
plt.tight_layout()
In [18]:
g = az.plot_trace(r_fic_noneighbors_strong, var_names=['Intercept',
                                                       'group_eff',
                                                       'cosine_fic_no_neighbors_strong_z',
                                                       'group_eff:cosine_fic_no_neighbors_strong_z'])
plt.tight_layout()
In [22]:
g = az.plot_trace(r_fic_nonames, var_names=['Intercept',
                                            'group_eff',
                                            'cosine_fic_no_mediators_z',
                                            'group_eff:cosine_fic_no_mediators_z'])
plt.tight_layout()

Cumulative posterior predictive check¶

Check if the model's predictions line up with the predictions in our observed data (i.e. there are no weird biases etc.)

In [23]:
m_fic.predict(r_fic, kind='pps')
g = az.plot_ppc(r_fic, kind='cumulative')
In [24]:
m_fic_filtered.predict(r_fic_filtered, kind='pps')
g = az.plot_ppc(r_fic_filtered, kind='cumulative')
In [4]:
m_fic_noneighbors_weak.predict(r_fic_noneighbors_weak, kind='pps')
g = az.plot_ppc(r_fic_noneighbors_weak, kind='cumulative')
In [19]:
m_fic_noneighbors_strong.predict(r_fic_noneighbors_strong, kind='pps')
g = az.plot_ppc(r_fic_noneighbors_strong, kind='cumulative')
In [7]:
m_fic_nonames.predict(r_fic_nonames, kind='pps')
g = az.plot_ppc(r_fic_nonames, kind='cumulative')

Convert notebook to html¶

In [17]:
convert_notebook('experiment_3')

[NbConvertApp] Converting notebook experiment_3.ipynb to html
[NbConvertApp] Writing 13989343 bytes to experiment_3.html

Jupyter notebook experiment_3 converted successfully.

In [ ]: